The two most widely used theories of elastic deformation
in solid materials are a microscopic approach based on
the statistical mechanics of lattices [1]}, [2]}, [3]} and
the quantum theory of solid-states [4]},
and a macroscopic approach based on
the classical continuum mechanics [5]}, [6]}.
Continuum elasticity is a phenomenological theory
representing continuum limit of lattice dynamics,
where the length-scales are much larger than inter-atomic distances.
Nonlocal elasticity theory is based on the assumption that
the forces between material points can be at long-range
in character, thus reflecting the long-range character
of interatomic and intermolecular forces.
In general, the nonlocal continuum models describe materials
whose behavior at any point depends on the states of
all other points in the media,
in addition to its own state and the state of external fields.
Such considerations are well-known in solid-state physics,
where the nonlocal interactions between the atoms and molecules
are prevalent in determining the properties of the media and materials.
